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Simplifying -2x2 + -14x + 8 = 0 Reorder the terms: 8 + -14x + -2x2 = 0 Solving 8 + -14x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -7x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -7x + -1x2)' equal to zero and attempt to solve: Simplifying 4 + -7x + -1x2 = 0 Solving 4 + -7x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -4 + 7x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 7x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 7x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 7x + x2 = 0 + 4 7x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 7x + x2 = 4 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 4 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 4 + 12.25 Combine like terms: 4 + 12.25 = 16.25 12.25 + 7x + x2 = 16.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (x + 3.5) equal to 4.031128874 and -4.031128874.Subproblem 1
x + 3.5 = 4.031128874 Simplifying x + 3.5 = 4.031128874 Reorder the terms: 3.5 + x = 4.031128874 Solving 3.5 + x = 4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 4.031128874 + -3.5 x = 4.031128874 + -3.5 Combine like terms: 4.031128874 + -3.5 = 0.531128874 x = 0.531128874 Simplifying x = 0.531128874Subproblem 2
x + 3.5 = -4.031128874 Simplifying x + 3.5 = -4.031128874 Reorder the terms: 3.5 + x = -4.031128874 Solving 3.5 + x = -4.031128874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -4.031128874 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -4.031128874 + -3.5 x = -4.031128874 + -3.5 Combine like terms: -4.031128874 + -3.5 = -7.531128874 x = -7.531128874 Simplifying x = -7.531128874Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.531128874, -7.531128874}Solution
x = {0.531128874, -7.531128874}
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